Abstract

Sparse signal representations and approximations from overcomplete dictionaries have become an
invaluable tool recently. In this paper, we develop a new, heuristic, graph-structured, sparse signal
representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries
and whose dictionary elements can be arranged in a hierarchy. Around this algorithm, we construct
a methodology for advanced image formation in wide-angle synthetic aperture radar (SAR), defining an
approach for joint anisotropy characterization and image formation. Additionally, we develop a coordinate
descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation
using that dictionary. The motivation is to characterize a phenomenon in wide-angle SAR that has not
been given much attention before: migratory scattering centers, i.e. scatterers whose apparent spatial
location depends on aspect angle. Finally, we address the topic of recovering solutions that are sparse in
more than one objective domain by introducing a suitable sparsifying cost function. We encode geometric objectives into SAR image formation through sparsity in two domains, including the normal parameter
space of the Hough transform.